A) \[-7<\lambda <1\]
B) \[\lambda >1\]
C) \[1<\lambda <7\]
D) \[-5<\lambda <1\]
Correct Answer: A
Solution :
Given,\[\overrightarrow{\mathbf{a}}=\lambda \widehat{\mathbf{i}}-7\widehat{\mathbf{j}}+3\widehat{\mathbf{k}},\,\,\overrightarrow{\mathbf{b}}=\lambda \widehat{\mathbf{i}}+\widehat{\mathbf{j}}+2\lambda \widehat{\mathbf{k}}\] \[\therefore \] \[\cos \theta =\frac{\overrightarrow{\mathbf{a}}\cdot \overrightarrow{\mathbf{b}}}{|\overrightarrow{\mathbf{a}}|\cdot |\overrightarrow{\mathbf{b}}|}\] \[=\frac{{{\lambda }^{2}}-7+6\lambda }{\sqrt{{{\lambda }^{2}}+49+9}\sqrt{{{\lambda }^{2}}+1+4{{\lambda }^{2}}}}<0\] \[\Rightarrow \] \[(\lambda +7)(\lambda -1)<0\] \[\Rightarrow \] \[-7<\lambda <1\]
You need to login to perform this action.
You will be redirected in
3 sec
